When two equal and opposite forces are applied to a body in a certain direction , the body extends along that direction and at the same time it cintracts along the perpandicular direction.
The fractional change in length of the body in the direction of the applied forces is longitudinal strain and fractional change in the perpandicular direction of the force applied is called lateral strain.
The ratio of lateral strain to the longitudinal strain is called poisson's ratio which is constant for material of that body.
So when a body is subjected to strain , say an elongation, it also suffers contraction in parpandicular direction.
Within elestic limits, lateral strain β is is proportional to longitudinal strain α.hence
longitudinal strain = α = Δl/l and
lateral strain = β = ΔD/D
hence poisson's ratio is σ =lΔD/DΔl